4. A manufacturer believes that the proportion of shipments of parts that arrive late is p = 0.6.

If a random sample of 12 orders shows that four or fewer arrived late, the hypothesis that

p = 0.6 will be rejected in favor of the alternative p<0.6. Use the binomial distribution to

answer the following.

(a) Find the probability of committing a type I error if the true proportion is 0.6.

(b) Find the probability of committing a type II error for the specific alternatives p = 0.3

and p = 0.5.